Magnetic Field Amplification in Young Galaxies

The Universe at present is highly magnetized, with fields of the order of a few 10^-5 G and coherence lengths larger than 10 kpc in typical galaxies like the Milky Way. We propose that the magnetic field was amplified to this values already during the formation and the early evolution of the galaxies. Turbulence in young galaxies is driven by accretion as well as by supernova (SN) explosions of the first generation of stars. The small-scale dynamo can convert the turbulent kinetic energy into magnetic energy and amplify very weak primordial magnetic seed fields on short timescales. The amplification takes place in two phases: in the kinematic phase the magnetic field grows exponentially, with the largest growth on the smallest non-resistive scale. In the following non-linear phase the magnetic energy is shifted towards larger scales until the dynamo saturates on the turbulent forcing scale. To describe the amplification of the magnetic field quantitatively we model the microphysics in the interstellar medium (ISM) of young galaxies and determine the growth rate of the small-scale dynamo. We estimate the resulting saturation field strengths and dynamo timescales for two turbulent forcing mechanisms: accretion-driven turbulence and SN-driven turbulence. We compare them to the field strength that is reached, when only stellar magnetic fields are distributed by SN explosions. We find that the small-scale dynamo is much more efficient in magnetizing the ISM of young galaxies. In the case of accretion-driven turbulence a magnetic field strength of the order of 10^-6 G is reached after a time of 24-270 Myr, while in SN-driven turbulence the dynamo saturates at field strengths of typically 10^-5 G after only 4-15 Myr. This is considerably shorter than the Hubble time. Our work can help to understand why present-day galaxies are highly magnetized.Comment: 13 pages, 8 figures; A&A in pres

The small-scale dynamo: Breaking universality at high Mach numbers

(Abridged) The small-scale dynamo may play a substantial role in magnetizing the Universe under a large range of conditions, including subsonic turbulence at low Mach numbers, highly supersonic turbulence at high Mach numbers and a large range of magnetic Prandtl numbers Pm, i.e. the ratio of kinetic viscosity to magnetic resistivity. Low Mach numbers may in particular lead to the well-known, incompressible Kolmogorov turbulence, while for high Mach numbers, we are in the highly compressible regime, thus close to Burgers turbulence. In this study, we explore whether in this large range of conditions, a universal behavior can be expected. Our starting point are previous investigations in the kinematic regime. Here, analytic studies based on the Kazantsev model have shown that the behavior of the dynamo depends significantly on Pm and the type of turbulence, and numerical simulations indicate a strong dependence of the growth rate on the Mach number of the flow. Once the magnetic field saturates on the current amplification scale, backreactions occur and the growth is shifted to the next-larger scale. We employ a Fokker-Planck model to calculate the magnetic field amplification during the non-linear regime, and find a resulting power-law growth that depends on the type of turbulence invoked. For Kolmogorov turbulence, we confirm previous results suggesting a linear growth of magnetic energy. For more general turbulent spectra, where the turbulent velocity v_t scales with the characteristic length scale as u_\ell\propto \ell^{\vartheta}, we find that the magnetic energy grows as (t/T_{ed})^{2\vartheta/(1-\vartheta)}, with t the time-coordinate and T_{ed} the eddy-turnover time on the forcing scale of turbulence. For Burgers turbulence, \vartheta=1/2, a quadratic rather than linear growth may thus be expected, and a larger timescale until saturation is reached.Comment: 10 pages, 3 figures, 2 tables. Accepted at New Journal of Physics (NJP

Chiral fermion asymmetry in high-energy plasma simulations

The chiral magnetic effect (CME) is a quantum relativistic effect that describes the appearance of an additional electric current along a magnetic field. It is caused by an asymmetry between the number densities of left- and right-handed fermions, which can be maintained at high energies when the chirality flipping rate can be neglected, for example in the early Universe. The inclusion of the CME in the Maxwell equations leads to a modified set of MHD equations. We discuss how the CME is implemented in the PENCIL CODE. The CME plays a key role in the evolution of magnetic fields since it results in a dynamo effect associated with an additional term in the induction equation. This term is formally similar to the $\alpha$ effect in classical mean-field MHD. However, the chiral dynamo can operate without turbulence and is associated with small spatial scales that can be, in the case of the early Universe, orders of magnitude below the Hubble radius. A chiral $\alpha_\mu$ effect has also been identified in mean-field theory. It occurs in the presence of turbulence but is not related to kinetic helicity. Depending on the plasma parameters, chiral dynamo instabilities can amplify magnetic fields over many orders of magnitude. These instabilities can affect the propagation of MHD waves, which is demonstrated by our DNS. We also study the coupling between the evolution of the chiral chemical potential and the ordinary chemical potential, which is proportional to the sum of the number densities of left- and right-handed fermions. An important consequence of this coupling is the emergence of chiral magnetic waves (CMWs). We confirm numerically that linear CMWs and MHD waves are not interacting. Our simulations suggest that the chemical potential has only a minor effect on the non-linear evolution of the chiral dynamo.Comment: 22 pages, 10 figures, in press at the GAFD special issue "Physics and Algorithms of the Pencil Code

Chiral magnetic anomaly and dynamos from spatial chemical potential fluctuations

Using direct numerical simulations, we show that a chiral magnetic anomaly can be produced just from initial spatially inhomogeneous fluctuations of the chemical potential, provided there is a small mean magnetic flux through the domain. The produced chiral asymmetry in the number densities of left- and right-handed fermions causes a chiral magnetic effect, the excitation of a chiral dynamo instability, the production of magnetically driven turbulence, and the generation of a large-scale magnetic field via the magnetic $\alpha$ effect from fluctuations of current helicity.Comment: 5 pages, 4 figure